%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM592+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:54 PM UTC 2026
% Result : Theorem 2.54s 1.29s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 8 unt; 2 def)
% Number of atoms : 373 ( 59 equ)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 456 ( 131 ~; 112 |; 178 &)
% ( 9 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 98 ( 81 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f91,axiom,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(xY)
& ! [X0] :
( aElementOf0(X0,xY)
<=> ( aElement0(X0)
& aElementOf0(X0,sdtlpdtrp0(xN,xi))
& X0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448_02) ).
fof(f93,axiom,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xX)
=> aElementOf0(X0,xY) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X0] :
( ( aSet0(X0)
& ( ( ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xX) )
| aSubsetOf0(X0,xX) )
& sbrdtbr0(X0) = xk )
| aElementOf0(X0,slbdtsldtrb0(xX,xk)) ) )
=> sdtlpdtrp0(xd,X0) = xu ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4545) ).
fof(f94,conjecture,
? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,xi))
& X2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
=> ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f95,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,xi))
& X2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
=> ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) = X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f104,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(xY)
& ! [X1] :
( aElementOf0(X1,xY)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(rectify,[],[f91]) ).
fof(f106,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xX)
=> aElementOf0(X0,xY) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X1] :
( ( aSet0(X1)
& ( ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xX) )
| aSubsetOf0(X1,xX) )
& sbrdtbr0(X1) = xk )
| aElementOf0(X1,slbdtsldtrb0(xX,xk)) ) )
=> sdtlpdtrp0(xd,X1) = xu ) ),
inference(rectify,[],[f93]) ).
fof(f107,plain,
~ ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) ) )
=> ( ( aSet0(X1)
& ! [X4] :
( aElementOf0(X4,X1)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(X1)
& ! [X5] :
( ( aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X5)
=> aElementOf0(X6,X1) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X5) = X0 ) ) ),
inference(rectify,[],[f95]) ).
fof(f134,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(xY)
& ! [X1] :
( aElementOf0(X1,xY)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(ennf_transformation,[],[f104]) ).
fof(f137,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xY)
| ~ aElementOf0(X0,xX) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X1] :
( sdtlpdtrp0(xd,X1) = xu
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,xX)
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,xX) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(xX,xk)) ) ) ),
inference(ennf_transformation,[],[f106]) ).
fof(f138,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xY)
| ~ aElementOf0(X0,xX) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X1] :
( sdtlpdtrp0(xd,X1) = xu
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,xX)
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,xX) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(xX,xk)) ) ) ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X4,X1) ) )
& ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ isCountable0(X1)
| ? [X5] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X5) != X0
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(ennf_transformation,[],[f107]) ).
fof(f140,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X4,X1) ) )
& ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ isCountable0(X1)
| ? [X5] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X5) != X0
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(flattening,[],[f139]) ).
fof(f245,definition,
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) )
| ~ sP18 ),
introduced(definition,[new_symbols(definition,[sP18])],[predicate_definition_introduction]) ).
fof(f246,definition,
! [X1] :
( ( ( ~ aSet0(X1)
| ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X4,X1) ) )
& ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sP18
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ sP19(X1) ),
introduced(definition,[new_symbols(definition,[sP19])],[predicate_definition_introduction]) ).
fof(f247,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( sP19(X1)
| ~ isCountable0(X1)
| ? [X5] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X5) != X0
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(definition_folding,[],[f140,f246,f245]) ).
fof(f319,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(xY)
& ! [X1] :
( ( aElementOf0(X1,xY)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,xY) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(nnf_transformation,[],[f134]) ).
fof(f320,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(xY)
& ! [X1] :
( ( aElementOf0(X1,xY)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,xY) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(flattening,[],[f319]) ).
fof(f324,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xY)
| ~ aElementOf0(X0,xX) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X1] :
( sdtlpdtrp0(xd,X1) = xu
| ~ aSet0(X1)
| ( ( ( ~ aElementOf0(sK44(X1),xX)
& aElementOf0(sK44(X1),X1)
& ~ aSubsetOf0(X1,xX) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(xX,xk)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(X2,sK44(X1))],[f138]) ).
fof(f325,plain,
! [X1] :
( ( ( ~ aSet0(X1)
| ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X4,X1) ) )
& ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sP18
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ sP19(X1) ),
inference(nnf_transformation,[],[f246]) ).
fof(f326,plain,
! [X0] :
( ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sP18
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ sP19(X0) ),
inference(rectify,[],[f325]) ).
fof(f327,plain,
! [X0] :
( ( ( ~ aSet0(X0)
| ( ~ aElementOf0(sK45(X0),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(sK45(X0),X0) ) )
& ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sP18
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ sP19(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(X1,sK45(X0))],[f326]) ).
fof(f331,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( sP19(X1)
| ~ isCountable0(X1)
| ? [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) != X0
& aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) ) ) ),
inference(rectify,[],[f247]) ).
fof(f332,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( sP19(X1)
| ~ isCountable0(X1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK46(X0,X1)) != X0
& aSet0(sK46(X0,X1))
& ! [X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,sK46(X0,X1)) )
& aSubsetOf0(sK46(X0,X1),X1)
& xk = sbrdtbr0(sK46(X0,X1))
& aElementOf0(sK46(X0,X1),slbdtsldtrb0(X1,xk)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(X2,sK46(X0,X1))],[f331]) ).
fof(f556,plain,
xd = sdtlpdtrp0(xC,xi),
inference(cnf_transformation,[],[f320]) ).
fof(f557,plain,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(cnf_transformation,[],[f320]) ).
fof(f580,plain,
! [X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(xX,xk))
| ~ aSet0(X1)
| sdtlpdtrp0(xd,X1) = xu ),
inference(cnf_transformation,[],[f324]) ).
fof(f584,plain,
isCountable0(xX),
inference(cnf_transformation,[],[f324]) ).
fof(f585,plain,
aSubsetOf0(xX,xY),
inference(cnf_transformation,[],[f324]) ).
fof(f588,plain,
aElementOf0(xu,xT),
inference(cnf_transformation,[],[f324]) ).
fof(f593,plain,
! [X0] :
( ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ sP19(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f600,plain,
! [X0,X1] :
( aElementOf0(sK46(X0,X1),slbdtsldtrb0(X1,xk))
| sP19(X1)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f332]) ).
fof(f604,plain,
! [X0,X1] :
( aSet0(sK46(X0,X1))
| sP19(X1)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f332]) ).
fof(f605,plain,
! [X0,X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK46(X0,X1)) != X0
| sP19(X1)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f332]) ).
fof(f763,plain,
! [X0,X1] :
( sdtlpdtrp0(xd,sK46(X0,X1)) != X0
| sP19(X1)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(superposition,[],[f605,f556]) ).
fof(f1506,plain,
! [X0] :
( ~ aSet0(sK46(X0,xX))
| xu = sdtlpdtrp0(xd,sK46(X0,xX))
| sP19(xX)
| ~ isCountable0(xX)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[],[f580,f600]) ).
fof(f1509,plain,
! [X0] :
( xu = sdtlpdtrp0(xd,sK46(X0,xX))
| ~ aSet0(sK46(X0,xX))
| sP19(xX)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f1506,f584]) ).
fof(f1510,plain,
! [X0] :
( xu != X0
| sP19(xX)
| ~ isCountable0(xX)
| ~ aElementOf0(X0,xT)
| ~ aSet0(sK46(X0,xX))
| sP19(xX)
| ~ aElementOf0(X0,xT) ),
inference(superposition,[],[f763,f1509]) ).
fof(f1512,plain,
! [X0] :
( xu != X0
| sP19(xX)
| ~ isCountable0(xX)
| ~ aElementOf0(X0,xT)
| ~ aSet0(sK46(X0,xX)) ),
inference(duplicate_literal_removal,[],[f1510]) ).
fof(f1513,plain,
! [X0] :
( xu != X0
| sP19(xX)
| ~ aElementOf0(X0,xT)
| ~ aSet0(sK46(X0,xX)) ),
inference(forward_subsumption_resolution,[],[f1512,f584]) ).
fof(f1514,plain,
( sP19(xX)
| ~ aElementOf0(xu,xT)
| ~ aSet0(sK46(xu,xX)) ),
inference(equality_resolution,[],[f1513]) ).
fof(f1515,plain,
( ~ aSet0(sK46(xu,xX))
| sP19(xX) ),
inference(forward_subsumption_resolution,[],[f1514,f588]) ).
fof(f1521,plain,
( sP19(xX)
| sP19(xX)
| ~ isCountable0(xX)
| ~ aElementOf0(xu,xT) ),
inference(resolution,[],[f1515,f604]) ).
fof(f1522,plain,
( sP19(xX)
| ~ isCountable0(xX)
| ~ aElementOf0(xu,xT) ),
inference(duplicate_literal_removal,[],[f1521]) ).
fof(f1523,plain,
( sP19(xX)
| ~ aElementOf0(xu,xT) ),
inference(forward_subsumption_resolution,[],[f1522,f584]) ).
fof(f1524,plain,
sP19(xX),
inference(forward_subsumption_resolution,[],[f1523,f588]) ).
fof(f1618,plain,
! [X0] :
( ~ aSubsetOf0(X0,xY)
| ~ sP19(X0) ),
inference(forward_demodulation,[],[f593,f557]) ).
fof(f1620,plain,
~ sP19(xX),
inference(resolution,[],[f1618,f585]) ).
fof(f1626,plain,
$false,
inference(forward_subsumption_resolution,[],[f1620,f1524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM592+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:40:02 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.54/1.29 % (1291874)Detected formulas, will run a generic FOF schedule.
% 2.54/1.29 % (1291881)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2091953233:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.29 % (1291883)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2367327267:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.29 % (1291882)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3951169481:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.29 % (1291879)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3314499360:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.29 % (1291880)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2155641336:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.29 % (1291884)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4059607429:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.29 % (1291885)dis-21_1_sil=8000:lcm=predicate:random_seed=3146823590:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.54/1.29 % (1291883)First to succeed.
% 2.54/1.29 % (1291883)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1291874"
% 2.54/1.29 % (1291882)Instruction limit reached!
% 2.54/1.29 % (1291882)------------------------------
% 2.54/1.29 % (1291882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.29 % (1291882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.29 % (1291882)CaDiCaL version: 2.1.3
% 2.54/1.29 % (1291882)Termination reason: Instruction limit
% 2.54/1.29 % (1291882)Termination phase: Saturation
% 2.54/1.29 % (1291882)Time elapsed: 0.070 s
% 2.54/1.29 % (1291882)Peak memory usage: 90 MB
% 2.54/1.29 % (1291882)Instructions burned: 109 (million)
% 2.54/1.29 % (1291885)Instruction limit reached!
% 2.54/1.29 % (1291885)------------------------------
% 2.54/1.29 % (1291885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.29 % (1291885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.29 % (1291885)CaDiCaL version: 2.1.3
% 2.54/1.29 % (1291885)Termination reason: Instruction limit
% 2.54/1.29 % (1291885)Termination phase: Saturation
% 2.54/1.29 % (1291885)Time elapsed: 0.065 s
% 2.54/1.29 % (1291885)Peak memory usage: 90 MB
% 2.54/1.29 % (1291885)Instructions burned: 130 (million)
% 2.54/1.29 % (1291884)Instruction limit reached!
% 2.54/1.29 % (1291884)------------------------------
% 2.54/1.29 % (1291884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.29 % (1291884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.29 % (1291884)CaDiCaL version: 2.1.3
% 2.54/1.29 % (1291884)Termination reason: Instruction limit
% 2.54/1.29 % (1291884)Termination phase: Saturation
% 2.54/1.29 % (1291884)Time elapsed: 0.110 s
% 2.54/1.29 % (1291884)Peak memory usage: 90 MB
% 2.54/1.29 % (1291884)Instructions burned: 139 (million)
% 2.54/1.29 % (1291893)lrs+10_1_sil=8000:sp=occurrence:random_seed=1195022810:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.54/1.29 % (1291894)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1415184352:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.54/1.29 % (1291894)Also succeeded, but the first one will report.
% 2.54/1.29 % (1291895)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1103270379:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.54/1.29 % (1291883)Refutation found. Thanks to Tanya!
% 2.54/1.29 % SZS status Theorem for theBenchmark
% 2.54/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.38 % (1291883)------------------------------
% 3.51/1.38 % (1291883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.38 % (1291883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.38 % (1291883)CaDiCaL version: 2.1.3
% 3.51/1.38 % (1291883)Termination reason: Refutation
% 3.51/1.38 % (1291883)Time elapsed: 0.035 s
% 3.51/1.38 % (1291883)Peak memory usage: 89 MB
% 3.51/1.38 % (1291883)Instructions burned: 58 (million)
% 3.51/1.38 % (1291883)------------------------------
% 3.51/1.38 % (1291883)------------------------------
% 3.51/1.38 % (1291874)Success in time 0.435 s
% 3.51/1.38 % Vampire exiting
%------------------------------------------------------------------------------